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A Tight Lower Bound for the Capture Time of the Cops and Robbers Game Brandt, Sebastian Emek, Yuval Uitto, Jara Wattenhofer, Roger cops and robbers capture time lower bound For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k >= 2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(n^{k + 1}), however, no non-trivial lower bounds were previously known; indeed, in their 2011 book, Bonato and Nowakowski ask whether this upper bound can be improved. In this paper, the question of Bonato and Nowakowski is answered on the negative, proving that the O(n^{k + 1}) bound is asymptotically tight for any constant k >= 2. This yields a surprising gap in the capture time complexities between the 1-cop and the 2-cop cases. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sebastian Brandt and Yuval Emek and Jara Uitto and Roger Wattenhofer 2017 Is Part Of LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2017.82 urn:nbn:de:0030-drops-74134 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.82 eng https://creativecommons.org/licenses/by/3.0/legalcode